1. Parallel & Cluster Computing Monte Carlo Henry Neeman, Director OU Supercomputing Center for Education & Research University of Oklahoma SC08 Education Program’s Workshop on Parallel & Cluster computing August 10-16 2008

2. SC08 Parallel & Cluster Computing: Monte Carlo University of Oklahoma, August 10-16 2008 2 Okla. Supercomputing Symposium 2006 Keynote: Dan Atkins Head of NSF’s Office of Cyber- infrastructure 2004 Keynote: Sangtae Kim NSF Shared Cyberinfrastructure Division Director 2003 Keynote: Peter Freeman NSF Computer & Information Science & Engineering Assistant Director 2005 Keynote: Walt Brooks NASA Advanced Supercomputing Division Director http://symposium2008.oscer.ou.edu/ 2007 Keynote: Jay Boisseau Director Texas Advanced Computing Center U. Texas Austin Tue Oct 7 2008 @ OU Over 250 registrations already! Over 150 in the first day, over 200 in the first week, over 225 in the first month. FREE! Parallel Computing Workshop Mon Oct 6 @ OU sponsored by SC08 FREE! Symposium Tue Oct 7 @ OU 2008 Keynote: José Munoz Deputy Office Director/ Senior Scientific Advisor Office of Cyber- infrastructure National Science Foundation

3. SC08 Parallel & Cluster Computing: Monte Carlo University of Oklahoma, August 10-16 2008 3 Embarrassingly Parallel An application is known as embarrassingly parallel if its parallel implementation: 1.can straightforwardly be broken up into roughly equal amounts of work per processor, AND 2.has minimal parallel overhead (e.g., communication among processors). We love embarrassingly parallel applications, because they get near-perfect parallel speedup, sometimes with modest programming effort. Embarrassingly parallel applications are also known as loosely coupled.

4. SC08 Parallel & Cluster Computing: Monte Carlo University of Oklahoma, August 10-16 2008 4 Monte Carlo Methods Monte Carlo is a European city where people gamble; that is, they play games of chance, which involve randomness. Monte Carlo methods are ways of simulating (or otherwise calculating) physical phenomena based on randomness. Monte Carlo simulations typically are embarrassingly parallel.

5. SC08 Parallel & Cluster Computing: Monte Carlo University of Oklahoma, August 10-16 2008 5 Monte Carlo Methods: Example Suppose you have some physical phenomenon. For example, consider High Energy Physics, in which we bang tiny particles together at incredibly high speeds. BANG! We want to know, say, the average properties of this phenomenon. There are infinitely many ways that two particles can be banged together. So, we can’t possibly simulate all of them.

6. SC08 Parallel & Cluster Computing: Monte Carlo University of Oklahoma, August 10-16 2008 6 Monte Carlo Methods: Example Suppose you have some physical phenomenon. For example, consider High Energy Physics, in which we bang tiny particles together at incredibly high speeds. BANG! There are infinitely many ways that two particles can be banged together. So, we can’t possibly simulate all of them. Instead, we can randomly choose a finite subset of these infinitely many ways and simulate only the subset.

7. SC08 Parallel & Cluster Computing: Monte Carlo University of Oklahoma, August 10-16 2008 7 Monte Carlo Methods: Example Suppose you have some physical phenomenon. For example, consider High Energy Physics, in which we bang tiny particles together at incredibly high speeds. BANG! There are infinitely many ways that two particles can be banged together. We randomly choose a finite subset of these infinitely many ways and simulate only the subset. The average of this subset will be close to the actual average.

8. SC08 Parallel & Cluster Computing: Monte Carlo University of Oklahoma, August 10-16 2008 8 Monte Carlo Methods In a Monte Carlo method, you randomly generate a large number of example cases (realizations) of a phenomenon, and then take the average of the properties of these realizations. When the realizations’ average converges (i.e., doesn’t change substantially if new realizations are generated), then the Monte Carlo simulation stops.

9. SC08 Parallel & Cluster Computing: Monte Carlo University of Oklahoma, August 10-16 2008 9 MC: Embarrassingly Parallel Monte Carlo simulations are embarrassingly parallel, because each realization is completely independent of all of the other realizations. That is, if you’re going to run a million realizations, then: 1.you can straightforwardly break up into roughly 1M / N p chunks of realizations, one chunk for each of the N p processors, AND 2.the only parallel overhead (e.g., communication) comes from tracking the average properties, which doesn’t have to happen very often.

10. SC08 Parallel & Cluster Computing: Monte Carlo University of Oklahoma, August 10-16 2008 10 Serial Monte Carlo Suppose you have an existing serial Monte Carlo simulation: PROGRAM monte_carlo CALL read_input(…) DO realization = 1, number_of_realizations CALL generate_random_realization(…) CALL calculate_properties(…) END DO CALL calculate_average(…) END PROGRAM monte_carlo How would you parallelize this?

11. SC08 Parallel & Cluster Computing: Monte Carlo University of Oklahoma, August 10-16 2008 11 Parallel Monte Carlo PROGRAM monte_carlo [MPI startup] IF (my_rank == server_rank) THEN CALL read_input(…) END IF CALL MPI_Bcast(…) DO realization = 1, number_of_realizations CALL generate_random_realization(…) CALL calculate_realization_properties(…) CALL calculate_local_running_average(...) END DO IF (my_rank == server_rank) THEN [collect properties] ELSE [send properties] END IF CALL calculate_global_average_from_local_averages(…) CALL output_overall_average(...) [MPI shutdown] END PROGRAM monte_carlo

12. SC08 Parallel & Cluster Computing: Monte Carlo University of Oklahoma, August 10-16 2008 12 Okla. Supercomputing Symposium 2006 Keynote: Dan Atkins Head of NSF’s Office of Cyber- infrastructure 2004 Keynote: Sangtae Kim NSF Shared Cyberinfrastructure Division Director 2003 Keynote: Peter Freeman NSF Computer & Information Science & Engineering Assistant Director 2005 Keynote: Walt Brooks NASA Advanced Supercomputing Division Director http://symposium2008.oscer.ou.edu/ 2007 Keynote: Jay Boisseau Director Texas Advanced Computing Center U. Texas Austin Tue Oct 7 2008 @ OU Over 250 registrations already! Over 150 in the first day, over 200 in the first week, over 225 in the first month. FREE! Parallel Computing Workshop Mon Oct 6 @ OU sponsored by SC08 FREE! Symposium Tue Oct 7 @ OU 2008 Keynote: José Munoz Deputy Office Director/ Senior Scientific Advisor Office of Cyber- infrastructure National Science Foundation

13. SC08 Parallel & Cluster Computing: Monte Carlo University of Oklahoma, August 10-16 2008 13 To Learn More http://www.oscer.ou.edu/ http://www.sc-conference.org/

14. Thanks for your attention! Questions?